The quadratic function above models the height above the ground h, in feet, of a projectile x seconds after it had been launched vertically. If is graphed in the xy-plane, which of the following represents the real-life meaning of the positive x-intercept of the graph?
A
The initial height of the projectile
B
The maximum height of the projectile
C
The time at which the projectile reaches its maximum height
D
The time at which the projectile hits the ground
Correct answer: D
Explanation
Choice D is correct. The positive x-intercept of the graph of is a point for which . Since models the height above the ground, in feet, of the projectile, a y-value of 0 must correspond to the height of the projectile when it is 0 feet above ground or, in other words, when the projectile is on the ground. Since x represents the time since the projectile was launched, it follows that the positive x-intercept, , represents the time at which the projectile hits the ground.
Choice A is incorrect and may result from misidentifying the y-intercept as a positive x-intercept. Choice B is incorrect and may result from misidentifying the y-value of the vertex of the graph of the function as an x-intercept. Choice C is incorrect and may result from misidentifying the x-value of the vertex of the graph of the function as an x-intercept.
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id cb_question_bank:e72ae0ec-edbf-47de-bbc0-5c50155b1bfb · question 7eed640d · IBN 019546-DC
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